I think it depends on your ROM .I recently checked mine and are in the following folder:
/data/data/com.android.providers.telephony/databases/.(telephony.db). You can try opening this .db file as text with a suitable file explorer and see if you can find them. (These are apns in the ROM by default)
I created a test apn manually and did a search, I learnt that its actually stored here: /data/data/com.android.settings/shared_prefs/com.android.settings_preferences.xml
(This xml also contains a lot of information found in settings but if you use a keyword search to try and find your manual apn, it will be much faster)
Some of the carrier apns happen to be auomatically added when you insert a new sim card, corresponding to the country, that is why they are stored in telephony database,I reckon. I hardly enter these apns manually even when I change a SIM card.